Let's analyze the given problem step by step to determine what the letter [tex]\( c \)[/tex] stands for in the formula:
[tex]\[ I = \frac{2yc}{m(n+1)} \][/tex]
1. Identify each variable in the formula:
- [tex]\( I \)[/tex]: Typically, [tex]\( I \)[/tex] represents the total interest.
- [tex]\( y \)[/tex]: Often represents the periodic payment (e.g., monthly payment).
- [tex]\( c \)[/tex]: This is the variable we need to identify.
- [tex]\( m \)[/tex]: Commonly stands for the number of months (or other periods, but here we'll consider months).
- [tex]\( n \)[/tex]: Usually represents the total number of months minus one.
2. Determine the context of each variable:
- Since [tex]\( I \)[/tex] is the total interest, it relates to how much interest is accrued over a period.
- [tex]\( y \)[/tex], being the periodic payment, helps in calculating the total amount paid over time.
- [tex]\( m \)[/tex] and [tex]\( n \)[/tex] relate to the timeframe of the loan in months.
3. Understand the structure of the formula:
- The formula implies that the interest [tex]\( I \)[/tex] is a result of some combination of these variables through multiplication and division.
- [tex]\( \frac{2yc}{m(n+1)} \)[/tex] means the numerator [tex]\( 2yc \)[/tex] has to do with the total amount financed or borrowed initially, in a manner influenced by the payment structure and time.
4. Interpret [tex]\( c \)[/tex]:
- The [tex]\( c \)[/tex] is multiplied by periodic payments [tex]\( y \)[/tex] and adjusted by a factor involving the number of periods. This suggests [tex]\( c \)[/tex] is likely related to the principal amount or amount borrowed initially, since the periodic payments and time frames work off this base value to generate total interest.
From these steps, we can conclude that [tex]\( c \)[/tex] stands for the amount financed, which means the initial principal amount of the loan or credit.
So, the correct answer is:
amount financed
